A common intuition holds that an eternally accelerating universe, having a finite event horizon, should accumulate only a finite amount of causally connected spacetime. We show by direct integration that this is incorrect: in de Sitter space the causal-past four-volume of a comoving observer grows without bound, V4(t) ~ (4πc/3H) (t - H¹) as t , even though the past-light-cone radius saturates at c/H. Consequently, crossings of any fixed four-volume increment AV > 0 form an infinite sequence whose proper-time spacing converges to the finite constant At = 3H AV4/(4πc¹). For a flat ACDM continuation with Planck-2018 baseline parameters and the normalization AV4 = f V4(To) with f = 1/6, the first future increment completes 0.580 Gyr from the present (cosmic age 14.375 Gyr) and the spacing decreases monotonically toward At = 40.1996 Myr. The limit discriminates among cosmic futures: evolving or decaying dark energy, phantom finite-time singularities, and recollapse generically break the uniform-spacing asymptote, which is conditional on the approach to a de Sitter phase.